The present invention pertains to the art of data processing and image reconstruction. It finds particular application in the reconstruction of magnetic resonance images and will be described with particular reference thereto. However, it is to be appreciated that the invention is also applicable to other imaging modalities including geophysics, land sat, computerized tomography, digital x-ray, optics, ultrasonics, and the like.
Heretofore, magnetic resonance imaging has been conducted in the presence of a strong magnetic field. An object to be imaged was positioned in an image region with the strong magnetic field passing substantially uniformly therethrough. Magnetic dipoles of nuclei disposed within the imaging region tended to align with the strong magnetic field. Resonance excitation radio frequency pulses were applied to the image region to cause the magnetic dipoles to precess about the strong magnetic field. As magnetic dipoles precessed, corresponding radio frequency resonance signals were generated thereby. Gradient magnetic fields were applied transverse to the main magnetic field to encode the frequency and phase of the radio frequency resonance signals in accordance with the spatial position of the precessing magnetic dipole which generated each resonance signal component. Various techniques, which are well known in the art, may be implemented to excite resonance and spatially encode the resonance signals.
In the spin-echo technique, the excitation pulses were cyclically applied and the magnetic dipoles were permitted to precess or undergo free induction decay therebetween. Square gradient pulses were applied such that the resonance signals were frequency encoded along one axis and phase encoded along an orthogonal axis. Resonance signal data was collected with uniform sampling in time to form views comprised of discrete electronic data lines. In this manner, data space was covered on a uniform grid. Each collected data line was operated upon by a two dimensional fast Fourier transform matrix to transform or map the data from the frequency domain to the spatial domain or image space. Commonly, numerous views were collected to extract information on spin density and relaxation times with high resolution and accuracy. Other reconstruction techniques such as hybrid imaging, echo planer imaging, and concentric circle imaging have also been used and are applicable to the present invention.
In order to reconstruct an accurate and precise image representation, it was necessary that the frequency domain data be uniform. Non-uniformities, errors, or distortions of the coverage in the data space introduced aliasing and other errors in the image representation. In particular, a Fourier transform assumes or treats input data as being uniformly sampled. Any non-uniformity in the sampling causes errors in the resultant image representation.
Heretofore, it was necessary to provide uniformly sampled data for the Fourier transform step. This necessitated accurate and precise linearity in the main magnetic field and the gradient magnetic fields. The systems were designed to limit other deviations such as eddy currents, motion, field inhomogeneities, non-uniform sampling, phase errors, gradient errors, and the like which also caused errors and aliasing.
In accordance with the present invention, an apparatus and method are provided for transforming non-uniform input data into a uniform image representation, when changes in time sampling which lead to uniform data space coverage can not be implemented.